Mach Cones in Quark Gluon Plasma

1. Mach Cones in Quark Gluon Plasma Jorge Casalderrey-Solana Lawrence Berkeley Laboratory

2. Jet-Medium Coupling What happens to the energy lost by jets? Leaves the interaction region being transferred to propagating modes: • Large angle induced radiation (Vitev, Polosa & Salgado) { Plasmon (Ruppert & Mueller) • Plasma modes Cherenkov ( Koch, Majumder & Wang, Dremin) Remains in the medium • Described as a parton cascade (Ma et al.) • Themalize (Stoecker , JCS, Teaney & Shuryak, • Renk & Ruppert, Chaudhuri & Heinz) Hydrodynamical behaviour  the medium reacts collectively

3. Hydrodynamic Modes Sound (φ) Propagating mode, cs Wave interference  Mach cone at Diffuson (Rμ) Not propagating mode Remembers source direction NR fluid dynamics  The strength of the two modes is set by the shape of the bullet What sets relative mode amplitude in Jet-Medium interaction?

4. Jet modification of hydro: Depostion/thermaliztion process One integral constraint The source is not unique: ρ (fm) ρ (fm) Function with zero integral x (fm) x (fm) Excitation Mechanisms Non isentropic excitations: the main excitation mechanism is entropy production and the flow field introduces vorticity. Isentropic excitations: No significant entropy production. Medium excitation by sound wave emission. The Eloss is quadratic in the amplitude.

5. Spectrum f f=p f=0 The fluid picture is not directly observed Spectrum: Cooper-Fry passocT fluid cell velocity Peaks at passocT║ v but broad angle distribution at low pT Excitation independent low passocT (T) angular dependence, the distribution from different fluid cells overlaps Peaks at back jet direction No large angle correlation at small passocT High passocT particles reflect the flow picture

6. Non Isentropic Excitations Diffuson  flow along jet direction dN/dydDf No large angle correlation p Df Chaudhuri & Heinz: Non linear hydro + source

7. Isentropic Excitations 4.0<PTTrig<6.0 GeV/c 0.15<PTAssoc<4.0 GeV/c Static Medium  Large dE/dx12 Gev/fm Expanding medium the  necessary dE/dx1.5 Gev/fm dN/dydDf (dilution of the medium) The correlations develops as passocT increases Df D The magnitude of the correlation decreases exponentially.

8. Expanding Medium The underlying flow v affects the directionality of the Mach cone (Satarov 05) Longitudinal flow  Elongation in y Radial flow broadens the peaks (misalignment of flow and jet) Renk + Ruppert : studies in a realistic background + BDMPS radiative losses Fraction f=0.75 of energy into θM θM updated with local cs Rapidity distribution of Back Jet P(y) Elongation due to longitudinal flow Dominated by Radial flow ║ Mach flow (Cooper-Fry) Observed 3-p signal (strong radial expansion destroys the cone)

9. Mach Angle from Transport Y. G. Ma, G. L. Ma et al. (06) AMPT Transport model: 22 parton cascade + recombination Large angle correlation is observed The signal has a partonic origin Hadronic re-scattering increases the magnitude of the correlation 3-particle analysis: the medium excitation is conical. It requires “long” partonic phase tp > 1.5 fm Large partonic σ  Hydro limit? collective effects? 22 interaction  Isentropic ? (no particle production)

10. Cherenkov radiation: w p Koch, Majumder, Wang (05) Dremin (05) At high T, plasma modes are time like  cannot be excited byω=vq If there are bound states in the plama: (space like gluon) Processes like lead to Large angle radiation happens mostly at low passoct as opposed to Mach cone. n(ω) >1 for ω inter-level spacing Heavy bound states are required for Cherenkov gluons at ω 1 GeV A similar mechanism in the plasmon (longitudinal gluon) can happen if it also becomes spacelike, εL>1 (Ruppert and Mueller)

11. Radiation at Large Angle Vitev (05) Induced gluon radiation is suppressed at small angle (interference) Smearing: Inclusive distribution do not show large angle correlations Polosa + Salgado: since ptrigT  passoTonly one gluon can be radiated Exclusive process  Sudakov  Stronger angular dependence than inclusive distribution. After smearing: Centrality dependence of the splitting parameter is reproduced. For low passocT becomes inclusive  no large angle correlations

12. Deflected Jets α (Armesto et al., Fries) Scattering of an energetic parton in the medium leads to a change in jet direction The collinear fragmentation along the back jet is the source of off π. At each event there are particle in only one side Clearly distinguishable through 3 particle correlation Chiu and Hwa (06) Follow path of the partons Random deflection (gaussian) At initial times σ/2=0.88 (large deflections)

13. Three Particle Correlations Au+Au 0-12% 13 θ* = 120 12 PHENIX Acceptance Indications of abnormal jets Star: signal along the off-diagonal consistent with conical structure

14. Conical Flow in AdS/CFT v=0.75 v=0.9 Mach cone 2 2 2 2 v=0.95 v=0.99 K┴ K┴ K┴ K┴ 1 1 1 1 0 0 0 0 2 2 2 2 KL KL KL KL 4 4 4 4 (Friess, Gubser, Michalogiorgakis, Pufu hep-th/0607022) String theory study of Heavy Quark motion in strongly coupled N=4 SYM { Herzog et al. Drag JCS & Teaney Gubser = Energy Density Looking at T00 they found the shock waves in N=4 SYM This is a dynamical model. No assumption about hydro- dynamical behavior is made!

15. CONCLUSIONS • Hydrodynamic description of deposited jet energy: Mach cone formation. • Particle spectrum reflects the cone (initial conditions!). • Transport calculations: compatible with the Mach cone • Mach like signals for plasma modes if n>1. • Large angle correlations from one gluon radiation. • pTasso dependence of D: • Deflected Jets Different three particle correlation. • Cherenkov: decreases (unless heavy bound states) • Mach cone and gluon radiation: increases

16. Buck up

17. Expansion effects: Amplitude Static fluid  the amplitude of sound waves decrease like v α 1/r v1 > v2 velocity field v1 v2 t1 t2 < T1 T2 T1 < T2 Expanding medium: also the fluids temperature lowers with t. The spectrum is controlled by v/T For RHIC, the evolution changes the fireball radius (from ~ 6fm to ~ 15 fm) and the c2s from 1/3 to 0.2  the amplitude v/T grows by a factor 3. Energy loss quadratic in the amplitude  necessary dE/dx  1.5 GeV/fm.

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